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- Title
NOTE ON SPECTRAL GAP AND WEIGHTED POINCARÉ INEQUALITIES FOR SOME ONE-DIMENSIONAL DIFFUSIONS.
- Authors
BONNEFONT, MICHEL; JOULIN, ALDÉRIC; YUTAO MA
- Abstract
We present some classical and weighted Poincaré inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric probability measures in dimension larger than 2. Our strategy is based on two main ingredients: on the one hand, the optimal constant in the desired weighted Poincaré inequality has to be rewritten as the spectral gap of a convenient Markovian diffusion operator, and on the other hand we use a recent result given by the two first authors, which allows to estimate precisely this spectral gap. In particular we are able to capture its exact value for some examples.
- Subjects
POINCARE series; VARIATIONAL inequalities (Mathematics); PROBABILITY measures; RIEMANNIAN manifolds; RIEMANNIAN metric
- Publication
ESAIM: Probability & Statistics, 2016, Vol 20, p18
- ISSN
1292-8100
- Publication type
Academic Journal
- DOI
10.1051/ps/2015019